1 |
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2 | var assert = require('assert'),
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3 | approx = require('../../../../tools/approx'),
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4 | math = require('../../../../index');
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5 |
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6 | describe('lup', function () {
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7 |
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8 | it('should decompose matrix, n x n, no permutations, array', function () {
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9 |
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10 | var m = [[2, 1], [1, 4]];
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11 |
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12 | var r = math.lup(m);
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13 |
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14 | assert.deepEqual(r.L.valueOf(), [[1, 0], [0.5, 1]]);
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15 |
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16 | assert.deepEqual(r.U.valueOf(), [[2, 1], [0, 3.5]]);
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17 |
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18 | assert.deepEqual(r.p, [0, 1]);
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19 |
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20 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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21 | });
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22 |
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23 | it('should decompose matrix, n x n, no permutations, sparse', function () {
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24 |
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25 | var m = math.matrix([[2, 1], [1, 4]], 'sparse');
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26 |
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27 | var r = math.lup(m);
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28 |
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29 | assert.deepEqual(r.L.valueOf(), [[1, 0], [0.5, 1]]);
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30 |
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31 | assert.deepEqual(r.U.valueOf(), [[2, 1], [0, 3.5]]);
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32 |
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33 | assert.deepEqual(r.p, [0, 1]);
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34 |
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35 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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36 | });
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37 |
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38 | it('should decompose matrix, n x n, no permutations, dense format', function () {
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39 |
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40 | var m = math.matrix([[2, 1], [1, 4]], 'dense');
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41 |
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42 | var r = math.lup(m);
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43 |
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44 | assert.deepEqual(r.L.valueOf(), [[1, 0], [0.5, 1]]);
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45 |
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46 | assert.deepEqual(r.U.valueOf(), [[2, 1], [0, 3.5]]);
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47 |
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48 | assert.deepEqual(r.p, [0, 1]);
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49 |
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50 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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51 | });
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52 |
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53 | it('should decompose matrix, m x n, m < n, no permutations, dense format', function () {
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54 | var m = math.matrix(
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55 | [
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56 | [2, 1, 1],
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57 | [1, 4, 5]
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58 | ]
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59 | );
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60 |
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61 | var r = math.lup(m);
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62 |
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63 | assert.deepEqual(
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64 | r.L,
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65 | math.matrix(
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66 | [
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67 | [1, 0],
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68 | [0.5, 1]
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69 | ]
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70 | ));
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71 |
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72 | assert.deepEqual(
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73 | r.U,
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74 | math.matrix(
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75 | [
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76 | [2, 1, 1],
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77 | [0, 3.5, 4.5]
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78 | ]
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79 | ));
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80 |
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81 | assert.deepEqual(r.p, [0, 1]);
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82 |
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83 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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84 | });
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85 |
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86 | it('should decompose matrix, m x n, m > n, no permutations, dense format', function () {
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87 | var m = math.matrix(
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88 | [
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89 | [8, 2],
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90 | [6, 4],
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91 | [4, 1]
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92 | ]
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93 | );
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94 |
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95 | var r = math.lup(m);
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96 |
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97 | assert.deepEqual(
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98 | r.L,
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99 | math.matrix(
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100 | [
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101 | [1, 0],
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102 | [0.75, 1],
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103 | [0.5, 0]
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104 | ]
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105 | ));
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106 |
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107 | assert.deepEqual(
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108 | r.U,
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109 | math.matrix(
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110 | [
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111 | [8, 2],
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112 | [0, 2.5]
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113 | ]
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114 | ));
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115 |
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116 | assert.deepEqual(r.p, [0, 1, 2]);
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117 |
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118 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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119 | });
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120 |
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121 | it('should decompose matrix, n x n, dense format', function () {
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122 | var m = math.matrix(
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123 | [
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124 | [16, -120, 240, -140],
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125 | [-120, 1200, -2700, 1680],
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126 | [240, -2700, 6480, -4200],
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127 | [-140, 1680, -4200, 2800]
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128 | ]
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129 | );
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130 |
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131 | var r = math.lup(m);
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132 |
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133 | approx.deepEqual(
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134 | r.L.valueOf(),
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135 | [
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136 | [1, 0, 0, 0],
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137 | [-0.5, 1, 0, 0],
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138 | [-0.5833333333333334, -0.7, 1, 0],
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139 | [0.06666666666666667, -0.4, -0.5714285714285776, 1]
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140 | ]);
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141 |
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142 | approx.deepEqual(
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143 | r.U.valueOf(),
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144 | [
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145 | [240, -2700, 6480, -4200],
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146 | [0, -150, 540, -420],
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147 | [0, 0, -42, 56],
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148 | [0, 0, 0, 4]
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149 | ]);
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150 |
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151 | assert.deepEqual(r.p, [3, 1, 0, 2]);
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152 |
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153 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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154 | });
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155 |
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156 | it('should decompose matrix, 3 x 3, zero pivote value, dense format', function () {
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157 | var m = math.matrix(
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158 | [
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159 | [1, 2, 3],
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160 | [2, 4, 6],
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161 | [4, 8, 9]
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162 | ]);
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163 |
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164 | var r = math.lup(m);
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165 |
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166 | approx.deepEqual(
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167 | r.L.valueOf(),
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168 | [
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169 | [1, 0, 0],
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170 | [0.5, 1, 0],
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171 | [0.25, 0, 1.0]
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172 | ]);
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173 |
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174 | approx.deepEqual(
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175 | r.U.valueOf(),
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176 | [
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177 | [4, 8, 9],
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178 | [0, 0, 1.5],
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179 | [0, 0, 0.75]
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180 | ]);
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181 |
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182 | assert.deepEqual(r.p, [2, 1, 0]);
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183 |
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184 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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185 | });
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186 |
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187 | it('should decompose matrix, 3 x 2, complex numbers, dense format', function () {
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188 | var m = math.matrix(
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189 | [
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190 | [math.complex(0, 3), 10],
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191 | [math.complex(0, 1), 1],
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192 | [math.complex(0, 1), 1]
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193 | ]);
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194 |
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195 | var r = math.lup(m);
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196 |
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197 | approx.deepEqual(
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198 | r.L.valueOf(),
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199 | [
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200 | [1, 0],
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201 | [math.complex(0.3333333, 0), 1],
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202 | [math.complex(0.3333333, 0), 1]
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203 | ]);
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204 |
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205 | approx.deepEqual(
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206 | r.U.valueOf(),
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207 | [
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208 | [math.complex(0, 3), 10],
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209 | [0, math.complex(-2.3333333333, 0)]
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210 | ]);
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211 |
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212 | assert.deepEqual(r.p, [0, 1, 2]);
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213 |
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214 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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215 | });
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216 |
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217 | it('should decompose matrix, m x n, m < n, no permutations, sparse', function () {
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218 | var m = math.matrix(
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219 | [
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220 | [2, 1, 1],
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221 | [1, 4, 5]
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222 | ],
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223 | 'sparse');
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224 |
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225 | var r = math.lup(m);
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226 |
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227 | assert.deepEqual(
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228 | r.L.valueOf(),
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229 | [
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230 | [1, 0],
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231 | [0.5, 1]
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232 | ]);
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233 |
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234 | assert.deepEqual(
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235 | r.U.valueOf(),
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236 | [
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237 | [2, 1, 1],
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238 | [0, 3.5, 4.5]
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239 | ]);
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240 |
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241 | assert.deepEqual(r.p, [0, 1]);
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242 |
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243 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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244 | });
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245 |
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246 | it('should decompose matrix, m x n, m > n, no permutations, sparse', function () {
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247 | var m = math.matrix(
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248 | [
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249 | [8, 2],
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250 | [6, 4],
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251 | [4, 1]
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252 | ],
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253 | 'sparse');
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254 |
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255 | var r = math.lup(m);
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256 |
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257 | assert.deepEqual(
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258 | r.L.valueOf(),
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259 | [
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260 | [1, 0],
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261 | [0.75, 1],
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262 | [0.5, 0]
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263 | ]);
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264 |
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265 | assert.deepEqual(
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266 | r.U.valueOf(),
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267 | [
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268 | [8, 2],
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269 | [0, 2.5]
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270 | ]);
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271 |
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272 | assert.deepEqual(r.p, [0, 1, 2]);
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273 |
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274 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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275 | });
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276 |
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277 | it('should decompose matrix, n x n, sparse', function () {
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278 | var m = math.matrix(
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279 | [
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280 | [16, -120, 240, -140],
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281 | [-120, 1200, -2700, 1680],
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282 | [240, -2700, 6480, -4200],
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283 | [-140, 1680, -4200, 2800]
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284 | ],
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285 | 'sparse');
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286 |
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287 | var r = math.lup(m);
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288 |
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289 | approx.deepEqual(
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290 | r.L.valueOf(),
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291 | [
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292 | [1, 0, 0, 0],
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293 | [-0.5, 1, 0, 0],
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294 | [-0.5833333333333334, -0.7, 1, 0],
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295 | [0.06666666666666667, -0.4, -0.5714285714285776, 1]
|
296 | ]);
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297 |
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298 | approx.deepEqual(
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299 | r.U.valueOf(),
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300 | [
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301 | [240, -2700, 6480, -4200],
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302 | [0, -150, 540, -420],
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303 | [0, 0, -42, 56],
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304 | [0, 0, 0, 4]
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305 | ]);
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306 |
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307 | assert.deepEqual(r.p, [3, 1, 0, 2]);
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308 |
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309 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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310 | });
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311 |
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312 | it('should decompose matrix, 3 x 3, zero pivote value, sparse', function () {
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313 | var m = math.matrix(
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314 | [
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315 | [1, 2, 3],
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316 | [2, 4, 6],
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317 | [4, 8, 9]
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318 | ],
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319 | 'sparse');
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320 |
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321 | var r = math.lup(m);
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322 |
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323 | approx.deepEqual(
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324 | r.L.valueOf(),
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325 | [
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326 | [1, 0, 0],
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327 | [0.5, 1, 0],
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328 | [0.25, 0, 1.0]
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329 | ]);
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330 |
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331 | approx.deepEqual(
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332 | r.U.valueOf(),
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333 | [
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334 | [4, 8, 9],
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335 | [0, 0, 1.5],
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336 | [0, 0, 0.75]
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337 | ]);
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338 |
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339 | assert.deepEqual(r.p, [2, 1, 0]);
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340 |
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341 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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342 | });
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343 |
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344 | it('should decompose matrix, 3 x 2, complex numbers, sparse', function () {
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345 | var m = math.matrix(
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346 | [
|
347 | [math.complex(0, 3), 10],
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348 | [math.complex(0, 1), 1],
|
349 | [math.complex(0, 1), 1]
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350 | ], 'sparse');
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351 |
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352 | var r = math.lup(m);
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353 |
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354 | approx.deepEqual(
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355 | r.L.valueOf(),
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356 | [
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357 | [1, 0],
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358 | [math.complex(0.3333333, 0), 1],
|
359 | [math.complex(0.3333333, 0), 1]
|
360 | ]);
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361 |
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362 | approx.deepEqual(
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363 | r.U.valueOf(),
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364 | [
|
365 | [math.complex(0, 3), 10],
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366 | [0, math.complex(-2.3333333333, 0)]
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367 | ]);
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368 |
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369 | assert.deepEqual(r.p, [0, 1, 2]);
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370 |
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371 | approx.deepEqual(math.multiply(_p(r.p), m).valueOf(), math.multiply(r.L, r.U).valueOf());
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372 | });
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373 |
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374 | |
375 |
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376 |
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377 | function _p(p) {
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378 |
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379 | var identity = math.eye(p.length);
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380 |
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381 | var data = [];
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382 |
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383 | for (var i = 0, l = p.length; i < l; i++) {
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384 |
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385 | data[p[i]] = identity._data[i];
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386 | }
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387 | return data;
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388 | }
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389 | });
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